Drilling through viscoelastic salt, shale and diatomite formations is a major challenge to avoid uncontrolled borehole shrinkage or expansion that can lead to stuck pipe or heavy fluid loss. Viscoelastic deformation or creep flow of material occurs whenever the octahedral stress exceeds its elastic limit that strongly depends on confining pressure as well as temperature. Rock failure occurs when the octahedral stress exceeds its plastic limit. Currently, the limiting octahedral stresses are obtained by testing a limited amount of core samples in a triaxial cell at various temperatures. The objective of the present invention is to provide a more reliable and cost-effective way of estimating these limiting octahedral stresses under in-situ conditions.
It is well known that mechanical disturbances can be used to establish elastic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain important information about the formations through which the waves have propagated. Parameters of compressional, shear and Stoneley waves, such as their velocity (or its reciprocal, slowness) in the formation and in the borehole, can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon resources. Recent studies of wave propagation in pre-stressed materials indicate that we can invert measured compressional and shear slowness data to estimate formation stress parameters.
An example of a logging device that has been used to obtain and analyze sonic logging measurements of formations surrounding an earth borehole is called a Dipole Shear Sonic Imager (“DSI”—trademark of Schlumberger), and is of the general type described in Harrison et al., “Acquisition and Analysis of Sonic Waveforms From a Borehole Monopole And Dipole Source For The Determination of Compressional and Shear Speeds and Their Relation to Rock Mechanical Properties and Surface Seismic Data,” Society of Petroleum Engineers, SPE 20557, 1990. In conventional use of the DSI logging tool, one can present compressional slowness, Δtc, shear slowness, Δts, and Stoneley slowness, Δtst, each as a function of depth, z. Slowness is the reciprocal of velocity and corresponds to the interval transit time typically measured by sonic logging tools.
An acoustic source in a fluid-filled borehole generates headwaves as well as relatively stronger borehole-guided modes. A standard sonic measurement system consists of placing a piezoelectric source and an hydrophone receivers inside a fluid-filled borehole. The piezoelectric source is configured in the form of either a monopole or a dipole source. The source bandwidth typically ranges from a 0.5 to 20 kHz. A monopole source generates primarily the lowest-order axi-symmetric mode, also referred to as the Stoneley mode, together with compressional and shear headwaves. In contrast, a dipole source primarily excites the lowest-order flexural borehole mode together with compressional and shear headwaves. The headwaves are caused by the coupling of the transmitted acoustic energy to plane waves in the formation that propagate along the borehole axis. An incident compressional wave in the borehole fluid produces critically refracted compressional waves in the formation. Those refracted along the borehole surface are known as compressional headwaves. The critical incidence angle θi=sin−1(Vf/Vc), where Vf is the compressional wave speed in the borehole fluid; and Vc is the compressional wave speed in the formation. As the compressional headwave travels along the interface, it radiates energy back into the fluid that can be detected by hydrophone receivers placed in the fluid-filled borehole. In fast formations, the shear headwave can be similarly excited by a compressional wave at the critical incidence angle θi=sin−1(Vf/Vs), where Vs is the shear wave speed in the formation. It is also worth noting that headwaves are excited only when the wavelength of the incident wave is smaller than the borehole diameter so that the boundary can be effectively treated as a planar interface. In a homogeneous and isotropic model of fast formations, as above noted, compressional and shear headwaves can be generated by a monopole source placed in a fluid-filled borehole for determining the formation compressional and shear wave speeds. It is known that refracted shear headwaves cannot be detected in slow formations (where the shear wave velocity is less than the borehole-fluid compressional velocity) with receivers placed in the borehole fluid. In slow formations, formation shear velocities are obtained from the low-frequency asymptote of flexural dispersion. There are standard processing techniques for the estimation of formation shear velocities in either fast or slow formations from an array of recorded dipole waveforms.